Hi everyone,

Your first homework assignment will be exclusively in the book (you do NOT have a WeBWorK assignment this week), and is due on Tuesday. Your first OpenLab Assignment is due on Thursday.

Welcome back,

Prof. Reitz

**Week 1 Assignments**

**Written work** due Tuesday Sept 2nd – Sec 1.1: 1, 12, 19, 26, 29, 35

**WeBWorK **– none

**OpenLab **– Register for the OpenLab and join this course (instructions provided in a separate post). “OpenLab #1: Advice from the Past” due Thurs Sept 4.

As reading through all the advice from the students who have taken this course, I have a mixed feeling. It seems that this course requires a solid foundation of algebra, a strong ability of abstract thinking and a well prepared attitude of self-discipline. All these give an impression that it might be a very challenging course. Haunting by this feeling, I feel an unnamed pressure since there is still a long way to go, especially, yesterday was the every first day of this battle of proofs and logic. However, all the essays from the previous students give me insightful advice that will help me to make learning this course be easier and effective.

First of all, more than two ex-students mentioned that proofs by induction are quite hard for them. They do not see the connection between P (k) => P (k+1) easily. To cope this problem, some of them suggest that thinking out of the box. I think that is very important for me. Personally, I believe that everyone has a relatively fixed thinking pattern. For example, every time when I open a door, I will instinctively choose to turn to the right side. Similarly, when I deal with math problems, I can say with certainty that I have my own preference of so-called strategies or techniques. This accustomed/ habitual thinking patterns sometimes do lead me to a chaotic situation which prevent me from being efficient. At this point, I appreciate Alan’s advice. I will keep in my minds that on the way of proofs, there are a lot of alternatives as if flying to one destine we can take off from different places of the earth, therefore, try to broke my own habit of thinking , I may see different beautiful view along the road that destinies to any proof.

Secondly, I agree with all the ex-students who have addressed the importance of doing homework. Personally, I think I am a beneficiaries of doing homework. Usually, students are used to falsely think that they are able to completely master the materials just because they well followed what their professors taught during the lecture time. Consequently, they ignore the homework. Through reading all the advice, I can learn that it is essential to do homework in order to reach the goal of achieving this course because homework provides us chance to practice what we have learned and shows us where our weak points are. Moreover, the procedure of doing homework is an indisputable process of strengthening prior knowledge. Therefore, I will definitely take this advice and put it into action.

Lastly, learning from prior mistakes is very necessary. Although none of the Ex-students mentioned that in their essays, I still feel the needs to point it out. As a self –retrospect, I confess that I often ignore the mistakes that I have made in the past papers, homework or tests as long as I am satisfied with the scores. Consequently, I become a realism of earning scores and an idealism of gaining knowledge, by which I mean, I pay more attention to the scores than the knowledge I missed to understand. Accumulatively, I feel as if I am standing on a shaking ground and very hard to step further.

All in all, all the advice is precious and meaningful, it likes a lighthouse. It serves us to navigate smoothly during the voyage of proofs and logic and keep us on the right route. I have to say it again that I really appreciate all the advice.